Die Meinung

Some Unpleasant Bull-Market Arithmetic

It seems that the excesses which inevitably build during periods of tranquility are building once again. Equity risk is growing as the bull market grows longer in the tooth.

Dylan Grice

Deutsche Version

Dylan Grice

Dylan Grice is co-founder of Calderwood Capital Research, an investment company specialising in portfolio construction and alternative investments. Prior to founding Calderwood, Dylan was the Head of Liquid Investments at Calibrium, a prominent private investment office based in Zurich. There, he was responsible for the management of the firm’s liquid portfolio, the research underpinning that portfolio, and the teams involved in the effort. Prior to joining Calibrium in 2014, Dylan was a part of the consistently top-ranked Global Strategy team at Société Générale, and was individually ranked first in the Extel Survey of institutional investor opinion in 2011 and 2012. Dylan started his career at Dresdner Kleinwort Wasserstein as an international economist and later prop trader. He is a graduate of Strathclyde University and the London School of Economics.
Alles anzeigen

Many credit spreads are trading through their pre-2007 tights even as credit quality appears to be deteriorating. Strange things are afoot in the market for equity-index-vol too, where concern is growing that the trading desks, which provide the «back end» for the structured products private banks sell to their clients, might be getting in too deep with regard to risks which are too non-linear to be manageable. Meanwhile, at Davos, Bridgewater’s Chuck Prince … sorry, Bob Prince pronounced the boom-bust cycle to be dead.

We don’t have a crystal ball. At Calderwood, we are portfolio constructors not market timers. We don’t build portfolios which depend on us being able to accurately gauge when the next recession will be. What we do need to be able to accurately gauge is the magnitude of risk we are underwriting. When the inevitable happens, our portfolio has to be robust to it.

And here we are increasingly concerned about equity risk, which we believe is growing as the bull market grows longer in the tooth. Specifically, there’s a relationship between expected returns and expected drawdown which is extremely important, but little understood. We often hear the complaint that people aren’t being sufficiently compensated for the risk they’re taking. We think the situation is much worse; people are taking far greater risks than they realise.

The only risk we care about

The theoretical way to think about risk and return is that they are two separate variables: on one hand you have your expected geometric mean (return) and on the other you have the expected volatility around that mean (risk), and changes in one don’t affect the other. According to this way of thinking, paying a price which is lower than underlying value is a good thing because it will give you a higher expected return, and therefore higher risk adjusted returns.

But since your maximum downside risk is still the same (i.e. 100%) you haven’t fundamentally taken less risk. By the same thinking, buying at a price which is higher than underlying value doesn’t mean you’re taking more risk, since you’re still on the hook for that same 100% theoretical maximum loss. The problem with overpaying is that you’re likely to have a lower expected return for the risk you took.

But this isn’t the way we look at it. The risk most of us care about isn’t price volatility per se but drawdown. I know there are those who differ and say that they don’t really care about short-term adverse prices moves, «it’s just noise» but in my experience such people are without exception big fibbers.

Getting through drawdowns is a necessary part of the job, but it’s certainly not one of the fun parts. No-one likes being in drawdown because no one likes the bona fide business risk drawdowns create for most asset managers. The standard way to fund the operating business is with the recurring management fee, which is charged as a percentage of aasets under management (AUM). A 50% drawdown therefore implies a 50% decline in the operating cashflow required to cover business overheads.

Fun and games

The easiest way to start thinking about drawdown risk is by imagining you’re playing a game in which you get to flip a fair coin. Heads wins $2, tails wins nothing, and it costs a dollar to play each round of the game (therefore its expected return is $0) What is the probability that you’ll be in drawdown after three flips? You get really unlucky and throw three consecutive losses (TTT). The chances of this happening are 0.5*0.5*0.5 = 0.5^3 = 0.125.

More likely though, you wouldn’t drawdown in a straight line. You’d be just as likely to throw THT or TTH or HTT as you would be to throw TTT. Indeed, out of eight possible coin flip sequences in total (2^3 = 8) there are four possible flip sequences which would see you end up underwater. So at the beginning of the game you know that you have a probability of 4/8 = 0.5 of being in drawdown after three flips. Easy.

But now let’s suppose that our expected return isn’t zero. Now let’s suppose that the coin is biased to land on heads 55% of the time meaning that the expected return of each flip is now positive (0.55* $2 - 0.45 * $0 - $1 = $0.10). Since the probability of a loss is now 0.45, the probability of consecutive losses is only 0.45^3 ≈ 0.091. So by increasing our expected return, we’ve decreased the probability of consecutive losses from our earlier 0.125 when the coin was fair.

Expected return and expected drawdown move in opposite directions

Indeed, when we do the arithmetic for the other combinations which would land us in drawdown territory after three throws, we find that in this newly calibrated positive expected return game the total probability of being in drawdown after 3 flips is only ≈ 0.43, where it had been 0.5 when our expected return was zero. Though this is a contrived and simplistic thought experiment, it’s nevertheless an important point: expected return and expected drawdown move in opposite directions.

Let’s make that point more relevant by applying it to today’s markets. Let’s think about drawdown probabilities in the most cyclically driven asset class of all: public equities. If we look at the history of the S&P500 Total Return index over the last century we get a decent feel for market drawdowns.

We can see the crashes of 2008 and 2001, as well as those in the rocky 1970s. And we can see the biggest of all, the Great Depression of the 1930s. It quickly becomes apparent that there’s a problem with the chart. The history we’re looking at is only one example of many possible alternative histories. What might have happened if we ran an alternative 20th Century in which the Great Depression was averted? Or another in which the Cuban Missile Crisis wasn’t?

Alternative scenarios

Of course, we can’t know. But we can guess. Since we know the rough statistical properties of the S&P500 over quite a long horizon we can, with some basic Monte Carlo routines, create our own artificial time-series data sets effectively simulating as many stock market histories as we want.

So instead of simulating coin flips like we did earlier, we’re going to simulate thousands of years of stock market returns which never happened. Then we can see what kind of drawdowns were experienced in these alternative histories.

Before we do this, a quick eyeball of Chart 2, which compares a typical simulated S&P index to the actual S&P 500 index (both total returns), and Chart 3, which compares the respective drawdowns show that while the fit isn’t perfect it’s in the ball park, and sufficient for the point we’re trying to illustrate.

So we are capable of simulating time-series which look and feel quite like the original, to some degree. Let’s start playing with it. The first thing we do is run our simulations to create time series which look and feel like the S&P500, but which have one significant difference: they are constructed to have different annualised returns.

One set of simulations will have 20% annualised returns over our 100yr alternative history, another will have 18%, another will have 16%, and so on, until the last one is programmed to have a 0% return.

High drawdown risk increases with time horizon

The second thing we do, when we have our new alternative histories, is check to see what kind of drawdowns they had. Of course, over a long enough time horizon what can happen will happen, so the longer the time horizon we choose to simulate the drawdown, the higher the expected max drawdown.

We choose a ten-year period. Chart 4 plots the expected drawdown and shows the same result to that of the simple coin flipping game: as expected returns increase (decrease), expected drawdown decreases (increases). This makes intuitive sense.

If the intrinsic value of an asset is growing on an underlying basis over time, the underlying mean path of its price will be to grind higher. Ordinary statistical variation will see it deviate from that mean path from time to time, and sometimes those deviations will be meaningful.

But the steeper the underlying mean growth path, the stronger the upward pull on the asset price, ensuring that falls from past peaks will be shallower. Conversely, if that underlying growth is low, or even zero there will be nothing to pull up any drawdown, and deviations from the mean will be much bigger.

Higher drawdown risk today than in 2007 and 1999

Anyway, so much for the simulations. What about the real world? The current Shiller earnings yield of the S&P500 is about 3%. If we add 1% of expected inflation to that, and maybe another 1% for real growth we get to around 5%. Also, the Shiller data goes back over a hundred years, so if we do this calculation for every month in the data we get a time-series history of what returns expectations would have been over the last 100 years or so.

Now, if we have a time-series of expected returns, we can plug that data into the curve we fitted in Chart 4 to map it onto a time-series of the expected maximum drawdown. We do this in Chart 5, which plots the time-series of expected maximum drawdowns over time along with the drawdowns actually experienced. It suggests that the expected maximum equity market drawdown today is deeper than it was in 2007, and even in 1999 at the height of the tech bubble.

What does it all mean?

On Bloomberg’s Odd Lots podcast, Benn Eifert told hosts Tracy Alloway and Joe Weisenthal his thesis on how banks’ equity vol trading desks were increasingly trapping themselves in a dangerous Faustian bargain. On the one hand, the structured product sales are very lucrative for the bank so long as markets are reasonably stable. On the other, if markets become unstable, banks might be on the hook for some disproportionately large losses.

In effect, says Eifert, banks are collectively very short the tails of the equity market. The 20% drawdown of Q4 2018 was a near run thing. «Everyone sitting on structured products desks was staring at their risk profile and thinking ‹If the market goes down by another 5% we’re screwed› because that’s where you get into all the non-linearity … but there will come a time when equity markets are down more than 20% peak-to-trough, and this market is very much set up to be a time bomb in that scenario.»

As we said in the beginning, stability is not stable. The signs of boom-time risk-taking and overreaching for yield are increasingly obvious. And now we know that lower expected returns must mean higher expected  drawdowns. Rebalance your portfolios towards less equity risk, before the market does it for you.